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October 2021 Collapsing ancient solutions of mean curvature flow
Theodora Bourni, Mat Langford, Giuseppe Tinaglia
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J. Differential Geom. 119(2): 187-219 (October 2021). DOI: 10.4310/jdg/1632506300

Abstract

We construct a compact, convex ancient solution of mean curvature flow in $\mathbb{R}^{n+1}$ with $O(1) \times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $\pi$ and in no smaller slab.

Funding Statement

The second author was partially supported by an Alexander von Humboldt fellowship.
The third author was partially supported by EPSRC grant no. EP/M024512/1.

Citation

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Theodora Bourni. Mat Langford. Giuseppe Tinaglia. "Collapsing ancient solutions of mean curvature flow." J. Differential Geom. 119 (2) 187 - 219, October 2021. https://doi.org/10.4310/jdg/1632506300

Information

Received: 2 May 2018; Accepted: 21 October 2019; Published: October 2021
First available in Project Euclid: 27 September 2021

Digital Object Identifier: 10.4310/jdg/1632506300

Rights: Copyright © 2021 Lehigh University

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Vol.119 • No. 2 • October 2021
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